Character Sheaves for Classical Graded Lie Algebras

In this note we study character sheaves for graded Lie algebras arising from inner automorphisms of special linear groups and Vinberg’s type Ⅱ classical graded Lie algebras.

Structures of Not-finitely Graded Lie Algebras Related to Generalized Heisenberg–Virasoro Algebras

In this paper, we study the structure theory of a class of not-finitely graded Lie alge- bras related to generalized Heisenberg-Virasoro algebras. In particular, the derivation algebras, the automorphism groups and the second cohomology groups of these Lie algebras are determined.

Modules of the Intermediate Series over Not-finitely Graded Lie Algebras W(Г)

Let W(Г)be a class of not-finitely graded Lie algebras related to generalized Virasoro algebras with basis{L_(α,i),C|α∈Г,i∈Z_(+)},which satisfies relations[L_(α,i),L_(β,j)]=L_(α+β,i+j)+(j-i)L_(α+β,i+j+1)+δ_(α+β,0)δ_(i+j),0α^(3)-α/12 C and[C,L_(α,i)]=0.In this paper,W(Г)-modules of the intermediate series satisfying some conditions are constructed and classified.We also obtain modules of the intermediate series over the related Lie superalgebra.

A new kind of graded Lie algebra and parastatistical supersymmetry

In this paper the usual Z2 graded Lie algebra is generalized to a new form, which may be called Z2,2 graded Lie algebra. It is shown that there exist close connections between the Z2,2 graded Lie algebra and parastatistics, so the Z2,2 can be used to study and analyse various symmetries and supersymmetries of the paraparticle systems.

一类Gerstenhaber代数的构造

For any K-algebra A,based on Hochschild complex and Hochschild coho-mology of A,we construct a new Gerstenhaber algebra,and give Gerstenhaber algebra epimorphism from the new Gerstenhaber algebra to the Gerstenhaber algebra of the Hochschild cohomology of A.

Graded Hochschild Cohomology of a Path Algebra with Oriented Cycles

The aim of this paper is to characterize the first graded Hochschild cohomology of a hereditary algebra whose Gabriel quiver is admitted to have oriented cycles. The interesting conclusion we have obtained shows that the standard basis of the first graded Hochschild cohomology depends on the genus of a quiver as a topological object. In this paper, we overcome the limitation of the classical Hochschild cohomology for hereditary algebra where the Gabriel quiver is assumed to be acyclic. As preparation, we first investigate the graded differential operators on a path algebra and the associated graded Lie algebra.

DG Poisson algebra and its universal enveloping algebra

We introduce the notions of differential graded(DG) Poisson algebra and DG Poisson module. Let A be any DG Poisson algebra. We construct the universal enveloping algebra of A explicitly, which is denoted by A^(ue). We show that A^(ue) has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over A is isomorphic to the category of DG modules over A^(ue). Furthermore, we prove that the notion of universal enveloping algebra A^(ue) is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.

Differential Graded Structures on Path Categories

In this paper, we consider the graded path category associated to a quiver. We investigate all n-differentials on such a category, and also study the associated graded Lie algebra. Moreover, a necessary and sufficient condition is given for the graded path categorv to admit a DG category structure.